242 Sir J. J. Thomson on the 



and E the enei 

 q and q-\-dq is 



and E the energy of the radiation with frequencies between 



8 *8 fhq v (hq\\* 27 



Denoting for brevity the function xKiQb) by T(«r) we may 

 write this as 



If X is the wave-length corresponding to the frequency q, 



and E A the energy in the radiation with wave-lengths 

 between X and X + c/X will be 



The value of $- which makes the coefficient of d\ in this 



expression a maximum is evidently such that if ~-i — x, 



then x is determined by the condition that x*'K 1 (tc) should 

 be a mnximum ; from the values of K T (V) given by Mr. Aldis 

 in the Tables already referred to 1 find that x = 2'&; hence 

 if \ m is the value of X which makes the energy between X and 

 \ + d\ a maximum at the temperature when dX is given, 

 we have 



/, 2tt _ 2j4 



\ m ad V 



Thus A m is a constant, and this constant is known with 

 considerable accuracy from the experiments which have been 

 made on the radiation from a black body. The value of this 

 constant found by hummer and Pringsheim * is 2940 x 10 " 4 . 

 If we call this quantity $, we have 



E x =f ^8ttT 2 (2-4(/>/X6^X (2) 



D X 



Since T(x) = xK 1 (,v) = — 1 when x is very small, we see 

 that for long waves 



E x varies as -^\d\. 

 A 



The same law is given by both Rayleigh's and Planck's 



values for E*. 



* Ferh, deutsch. phys, Ges. i. p. 230. 



